I used to do these fairly complicated sales contracts for the company, and because it has potential money attached to it, it's always "urgent". There were, say, 10 sales people globally and just me doing these contracts. I told them that if their stuff is actually urgent, to spam my email with the urgency or I'll just never get around to it. Of course, if they asked ahead of time, I usually prioritised those first because they were responsible.

Worked like a charm. If you asked a month ago and didn't follow up, you obviously don't care about that one. Get back to me when you actually care.

It was super stressful. Urgent has no actual meaning anymore.